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variants of this functions
EllipticPi






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticPi[n,z,m] > Series representations > Generalized power series > Expansions on branch cuts > Formulas for vertical intervals > For Re(z0/2 Pi-3/4) ∈ Z





http://functions.wolfram.com/08.06.06.0067.01









  


  










Input Form





EllipticPi[n, z, m] \[Proportional] ((2 (2 Re[Subscript[z, 0]/(2 Pi) - 3/4] + 1) EllipticPi[n, m] + (1/Sqrt[m]) EllipticPi[n/m, 1/m]) (1 - Exp[(-Pi) I (Floor[1/4 + Arg[z - Subscript[z, 0]]/(2 Pi)] + Floor[1/4 - Arg[z - Subscript[z, 0]]/(2 Pi)])]) + Exp[(-Pi) I (Floor[1/4 + Arg[z - Subscript[z, 0]]/(2 Pi)] + Floor[1/4 - Arg[z - Subscript[z, 0]]/(2 Pi)])] EllipticPi[n, Subscript[z, 0], m]) (1 + O[z - Subscript[z, 0]]) /; (z -> Subscript[z, 0]) && Element[Re[Subscript[z, 0]/(2 Pi) - 3/4], Integers]










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02





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